Neural approximators for functional optimization

Functional optimization problems can be solved analytically only if special assumptions are verified. The approximation method that we propose for the general case is based on the following steps: 1) the decision law is constrained to assume a fixed structure, in which a certain number of free parameters must be optimized, and this enables the functional optimization problem to be reduced to a nonlinear programming one; 2) as a fixed structure, we choose, among various nonlinear approximators, the input/output mapping of multilayer feedforward neural networks; and 3) the resulting nonlinear programming problem is characterized by a highly complex cost function. We propose to minimize it by stochastic programming algorithms. As test-beds for the solving technique, we address a stochastic optimal control problem and an estimation problem, whose solutions are traditionally regarded as difficult tasks